On normal solvability of the riemann problem with singular coefficient

M. Rakowski, Ilya Spitkovsky

Research output: Contribution to journal › Article

Abstract

Suppose G is a singular matrix function on a simple, closed, rectifiable contour F. We present a necessary and sufficient condition for normal solvability of the Riemann problem with coefficient G in the case where G admits a spectral (or generalized Wiener-Hopf) factorization G+ΛG- with G±1 essentially bounded. The boundedness of G±1 is not required when Γ takes injective values a.e. on F.

title = "On normal solvability of the riemann problem with singular coefficient",

abstract = "Suppose G is a singular matrix function on a simple, closed, rectifiable contour F. We present a necessary and sufficient condition for normal solvability of the Riemann problem with coefficient G in the case where G admits a spectral (or generalized Wiener-Hopf) factorization G+ΛG- with G±1 essentially bounded. The boundedness of G±1 is not required when Γ takes injective values a.e. on F.",

author = "M. Rakowski and Ilya Spitkovsky",

year = "1997",

month = "12",

day = "1",

language = "English (US)",

volume = "125",

pages = "815--826",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "3",

}

TY - JOUR

T1 - On normal solvability of the riemann problem with singular coefficient

AU - Rakowski, M.

AU - Spitkovsky, Ilya

PY - 1997/12/1

Y1 - 1997/12/1

N2 - Suppose G is a singular matrix function on a simple, closed, rectifiable contour F. We present a necessary and sufficient condition for normal solvability of the Riemann problem with coefficient G in the case where G admits a spectral (or generalized Wiener-Hopf) factorization G+ΛG- with G±1 essentially bounded. The boundedness of G±1 is not required when Γ takes injective values a.e. on F.

AB - Suppose G is a singular matrix function on a simple, closed, rectifiable contour F. We present a necessary and sufficient condition for normal solvability of the Riemann problem with coefficient G in the case where G admits a spectral (or generalized Wiener-Hopf) factorization G+ΛG- with G±1 essentially bounded. The boundedness of G±1 is not required when Γ takes injective values a.e. on F.